Formal Languages Questions Medium
Decidability and semi-decidability are two important concepts in the field of formal languages and computability theory.
Decidability refers to the property of a language or problem being solvable by an algorithm, where the algorithm will always halt and provide a correct answer, either "yes" or "no". In other words, a language is decidable if there exists a Turing machine that can determine whether a given input belongs to the language or not.
On the other hand, semi-decidability (also known as computability or partially decidable) refers to the property of a language or problem being solvable by an algorithm that may not always halt. A language is semi-decidable if there exists a Turing machine that can recognize whether a given input belongs to the language, but it may not halt or provide an answer for inputs that do not belong to the language.
In summary, the main difference between decidability and semi-decidability lies in the behavior of the algorithms used to solve the language or problem. Decidability guarantees that an algorithm will always halt and provide a correct answer, while semi-decidability allows for non-halting behavior, where the algorithm may not provide an answer for inputs that do not belong to the language.